adaptive dsp algorithms for umts: blind adaptive mmse and

Adaptive DSP Algorithms for UMTS:

Blind Adaptive MMSE and PIC Multiuser

Detection

–

Adaptive Wireless Networking (AWGN)

Jordy [email protected]

University of Twentefaculty of Electrical Engineering, Mathematics & Computer Science

Signals and Systems groupP.O. Box 217, 7500 AE Enschede

the Netherlands

November 17, 2003

Abstract

A study of the application of blind adaptive Minimum Mean Square Er-ror (MMSE) and Parallel Interference Cancellation (PIC) multiuser detec-tion techniques to Wideband Code Division Multiple Access (WCDMA),the physical layer of Universal Mobile Telecommunication System (UMTS),has been performed as part of the Freeband Adaptive Wireless Networkingproject. This study was started with an analysis of Code Division Multi-ple Access (CDMA) and conventional CDMA detection. After that blindadaptive MMSE and PIC detection have been analyzed for general CDMAsystems. Then the differences between WCDMA and general CDMA wereanalyzed and the results have been used to determine how blind adaptiveMMSE and PIC can be implemented in WCDMA systems.

Blind adaptive MMSE has been implemented in WCDMASim, a WCDMAsimulator and some preliminary simulation results obtained with this simula-tor are presented. These simulation results do not yet show the performancethat was expected of blind adaptive MMSE detection based on simulationresults obtained in previous research. The cause for these unexpected resultsis not yet known and will be the subject of further research.

Implementation of PIC detection in WCDMASim was found to requirechanges to the architecture of the WCDMASim simulator. Implementa-tion of these changes and solving the problems with blind adaptive MMSEdetection are considered for future work.

Contents

1 Introduction 1

2 CDMA and Conventional CDMA Detection 32.1 CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Continuous-time Synchronous CDMA Model . . . . . . . . . 62.3 Discrete-time CDMA Model and Conventional Detection . . . 6

3 Blind Adaptive MMSE Detection 93.1 Linear Multiuser Detectors . . . . . . . . . . . . . . . . . . . 93.2 Minimizing Mean Output Energy . . . . . . . . . . . . . . . . 103.3 Stochastic Gradient Decent Method . . . . . . . . . . . . . . 123.4 Adaptive Implementation . . . . . . . . . . . . . . . . . . . . 13

4 PIC Detection 174.1 Decision-driven Detectors . . . . . . . . . . . . . . . . . . . . 174.2 PIC Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3 PIC Implementation . . . . . . . . . . . . . . . . . . . . . . . 204.4 Amplitude Estimation . . . . . . . . . . . . . . . . . . . . . . 234.5 Partial Cancellation PIC . . . . . . . . . . . . . . . . . . . . . 24

5 WCDMA Uplink Model 275.1 WCDMA Uplink . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 General WCDMA Uplink Model . . . . . . . . . . . . . . . . 28

6 Blind Adaptive MMSE Detection for WCDMA 316.1 Synchronous AWGN Short Code WCDMA Uplink Model . . 316.2 Blind Adaptive MMSE for Synchronous AWGN WCDMA . . 326.3 Asynchronous WCDMA Systems and Other Channel Models 34

7 PIC Detection for WCDMA 377.1 Synchronous AWGN WCDMA Uplink Model . . . . . . . . . 377.2 PIC for Synchronous AWGN WCDMA . . . . . . . . . . . . . 387.3 Asynchronous WCDMA Systems and Other Channel Models 39

Adaptive Wireless Networking (AWGN) v

CONTENTS

8 WCDMASim 418.1 WCDMASim . . . . . . . . . . . . . . . . . . . . . . . . . . . 418.2 WCDMASim Uplink Simulator . . . . . . . . . . . . . . . . . 41

8.2.1 Initialization Phase Block . . . . . . . . . . . . . . . . 428.2.2 Desired Signal Block . . . . . . . . . . . . . . . . . . . 438.2.3 MAI Signal Block . . . . . . . . . . . . . . . . . . . . 438.2.4 Rake Receiver Block . . . . . . . . . . . . . . . . . . . 44

8.3 Extending WCDMASim . . . . . . . . . . . . . . . . . . . . . 448.3.1 Implementing Blind Adaptive MMSE Detection . . . . 448.3.2 Implementing PIC Detection . . . . . . . . . . . . . . 468.3.3 Additional Changes . . . . . . . . . . . . . . . . . . . 47

9 Simulation Results 499.1 Data Stream to Received Signal . . . . . . . . . . . . . . . . . 499.2 Long and Short Scramble Code Comparison . . . . . . . . . . 539.3 Conventional and Blind Adaptive MMSE Detector Comparison 53

10 Conclusions and Recommendations 5510.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5510.2 Recommendations and Future Work . . . . . . . . . . . . . . 57

vi Adaptive DSP Algorithms for UMTS

List of Figures

2.1 Direct-sequence spread-spectrum transmitter. . . . . . . . . . 42.2 Direct-sequence spread-spectrum receiver. . . . . . . . . . . . 42.3 Matched filter bank. . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 Blind adaptive MMSE detector. . . . . . . . . . . . . . . . . . 15

4.1 SIC detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2 Two stage PIC detector. . . . . . . . . . . . . . . . . . . . . . 194.3 S stage narrowband PIC detector. . . . . . . . . . . . . . . . 214.4 S stage wideband PIC detector. . . . . . . . . . . . . . . . . . 22

5.1 WCDMA uplink spreading and modulation. . . . . . . . . . . 28

8.1 WCDMASim uplink simulator structure [1]. . . . . . . . . . . 428.2 Short scrambling sequence generation . . . . . . . . . . . . . 45

9.1 From data streams to received signal in the WCDMASimsimulator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

9.2 From data streams to received signal in the WCDMASimsimulator (continued). . . . . . . . . . . . . . . . . . . . . . . 51

9.3 Bit-error-rate comparison between a long and a short codeWCDMA system. . . . . . . . . . . . . . . . . . . . . . . . . . 52

9.4 Bit-error-rate comparison between conventional and blind adap-tive MMSE detection. . . . . . . . . . . . . . . . . . . . . . . 54

Adaptive Wireless Networking (AWGN) vii

Acronyms

AWGN Additive White Gaussian NoiseBER Bit-Error-RateCDMA Code Division Multiple AccessDPCCH Dedicated Physical Control ChannelDPDCH Dedicated Physical Data ChannelDPDCHs Dedicated Physical Data ChannelsDSP Digital Signal ProcessingFDD Frequency Division DuplexFPFAs Field Programmable Function ArraysFPGAs Field Programmable Gate ArraysGPPs General Purpose ProcessorsNRZ Non-Return-to-ZeroMAI Multiple Access InterferenceMIC Multistage Interference CancellationMMSE Minimum Mean Square ErrorMOE Mean Output EnergyMSE Mean Square ErrorOVSF Orthogonal Variable Spreading FactorPIC Parallel Interference CancellationSIC Successive Interference CancellationSNR Signal to Noise RatioSNRs Signal to Noise RatiosTFCI Transport Format Combination IndicatorTPC Transmission Power ControlFBI Feedback InformationUMTS Universal Mobile Telecommunication SystemWCDMA Wideband Code Division Multiple Access

Adaptive Wireless Networking (AWGN) ix

Chapter 1

Introduction

The Freeband Adaptive Wireless Networking (AWGN) project aims to de-velop methods and technologies that can be used to design efficient adaptableand reconfigurable base stations and terminals for third and fourth gener-ation wireless communication systems, as for example UMTS. In order toachieve this, the project consists of two activities.

The first activity is the mapping of (different) communication systemson a platform of heterogeneous reconfigurable architectures. The platformis heterogenous in the sense that Digital Signal Processing (DSP) is per-formed on General Purpose Processors (GPPs), Field Programmable GateArrays (FPGAs) and Field Programmable Function Arrays (FPFAs). Thesearchitectures are all reconfigurable in the sense that they can be repro-grammed in-system with new DSP algorithms.

The second activity is the study and development of adaptive DSP al-gorithms for UMTS. These algorithms are adaptive in the sense that theyallow the communication system to adapt to changing environmental con-ditions (e.g. changing numbers of users in a cell or varying noise figures dueto reflections or user movements) as well as changing user demands.

This report is the first report of the ‘adaptive DSP algorithms for UMTSactivity’. The focus of the research described in this report is on multiuserdetection algorithms which allow a UMTS base station to adapt to thenumber of active users in a cell and reduce the influence of Multiple AccessInterference (MAI).

MAI, the interference that the signal of a user experiences caused by thesignals of the other users on a channel, is inherent in cellular wireless CodeDivision Multiple Access (CDMA) communications systems. ConventionalCDMA receivers treat MAI as if it were additive random noise. In mul-tiuser detection information about the signals of the other users is used toimprove detection of the signal of each individual user. In previous research([2], [3]) blind adaptive Minimum Mean Square Error (MMSE) multiuserdetection and Parallel Interference Cancellation (PIC) multiuser detection

Adaptive Wireless Networking (AWGN) 1

Chapter 1. Introduction

were found to be two of the more promising multiuser detection techniquesfor CDMA communications systems. In the CDMA model that was usedin this previous research however, a lot of the effects that are present inan actual cellular wireless CDMA communications system, as for examplefading and multipath, were ignored. Therefor in this report, blind adaptiveMMSE and PIC multiuser detection will be studied using an accurate modelof the uplink of Wideband Code Division Multiple Access (WCDMA), thephysical layer of the Universal Mobile Telecommunication System (UMTS)communications system. The goals of this study are to:

1. Determine if the blind adaptive MMSE and PIC multiuser detectiontechniques can be applied to WCDMA.

2. Implement blind adaptive MMSE and PIC multiuser detection in aWCDMA simulator.

3. Determine the performance of blind adaptive MMSE and PIC mul-tiuser detection in WCDMA trough simulations and asses the effectsof detector parameter choices.

In a later phase of the project the obtained results can be used to studythe implementation related issues of blind adaptive MMSE and PIC mul-tiuser detection. This serves as a preparation for the implementation ofthese detection techniques in a test-bed. Eventually this will lead to animplementation of blind adaptive MMSE and PIC multiuser detection forUMTS on a heterogenous reconfigurable architecture.

Chapter 2 of this report starts with a general description of CDMA.After that the CDMA system models that are frequently used in literaturedescribing multiuser detection are given. These CDMA system models werealso used in the mentioned previous research. Finally Chapter 2 containsa description of conventional CDMA detection. The models described inChapter 2 are used to describe blind adaptive MMSE detection in Chapter3 and PIC detection in Chapter 4. In Chapter 5 a mathematical modelfor WCDMA is developed. This WCDMA model is used to describe blindadaptive MMSE detection for WCDMA in Chapter 6 and PIC detection forWCDMA in Chapter 7. Chapter 8 describes the simulator that is used tostudy the performance of blind adaptive MMSE and PIC detection. Thischapter also describes the extensions to the simulator that have been imple-mented to support simulation of these two detection techniques. In Chapter9 some preliminary simulation results are presented. Finally in Chapter 10,the conclusions and recommendations that can be drawn from the researchdescribed in this report are given. Chapter 10 also gives some directions forfuture research.

2 Adaptive DSP Algorithms for UMTS

Chapter 2

CDMA and ConventionalCDMA Detection

In this chapter first a general description of CDMA is given. After thatcontinuous- and discrete-time CDMA system models are given that are fre-quently used in literature describing multiuser detection. These system mod-els will be used to describe blind adaptive MMSE and PIC detection in thenext two chapters. At the end of this chapter conventional CDMA detectionis discussed briefly.

2.1 CDMA

CDMA uses direct-sequence spread-spectrum techniques to achieve efficientmultiple access communications. In a direct sequence spread spectrum trans-mitter each bit of a binary nonreturn-to-zero information signal is modu-lated by one period of a binary nonreturn-to-zero pseudo-random sequenceto generate the transmitted signal, see Figure 2.1. This pseudo-random se-quence is also referred to as signature sequence, signature waveform, or in anolder terminology code, explaining the term code-division multiple access.The pseudo-random sequence is composed of elementary pulses of durationTc commonly referred to as chips. Because the duration of a chip of thepseudo-random sequence is usually a lot shorter than the duration T of abit of the information signal the modulated signal will be a wide-band signalwith nearly the same spectrum as the pseudo-random sequence. The band-width expansion ratio T/Tc is also know as the spreading gain. In a CDMAsystem the particular signature sequence of a user identifies the particularpoint-to-point channel corresponding to that user.

CDMA receivers employ the signature sequence of a user as the keyto recover the transmitted information. Detection of the transmitted datais accomplished with a correlation demodulator driven by a synchronizedreplica of the signature waveform used at the transmitter, see Figure 2.2.


Chapter 2. CDMA and Conventional CDMA Detection

Figure 2.1: Direct-sequence spread-spectrum transmitter.

The by design low correlation between the signature waveforms of the dif-ferent users gives the CDMA system its multiple access properties.

In an ideal CDMA system orthogonal signature sequences would be used.A CDMA system using orthogonal signature sequences will cancel out allMultiple Access Interference (MAI) and yield single user performance. How-ever, fully orthogonal systems are not practical for two reasons. First, for agiven limited number of chips there only exist a limited number of orthog-onal signature sequences. Secondly, and more importantly, if the users arenot transmitting synchronously, the signature sequences are out of phase andloose their orthogonal property. CDMA systems normally use shift-registersequences or combinations of shift-register sequences for their signature se-

Figure 2.2: Direct-sequence spread-spectrum receiver.


2.1. CDMA

quences. It is not possible to obtain signature sequences for any pair of usersthat are orthogonal for all time offsets using this method.

Not having completely orthogonal signature sequences would not cause adramatic performance decrease, if the received power of the interfering signalis smaller than the received power of the signal of the desired user. However,if the interfering signals are much stronger than the signal of the desireduser, proper detection becomes impossible. This scenario occurs often inpractical systems. For example consider the link from a cellular phone to abase station. If one cellular phone is transmitting from a position close tothe base station and another cellular phone is transmitting from a positionfurther away from the base station, then the received power of the signal ofthe first cellular phone will be higher than that of the distant cellular phone,assuming that their transmit powers are equal. Thus, the detection of thedistant user will result in a severe increase in bit errors. This situation isgenerally called the near-far problem.

A natural solution to the near-far problem is the use of power control.The power control system compares the received power levels. It uses acontrol channel to transmit power status information to the cellular phones.The cellular phone will adapt its transmitting power in such a way thatthe received power at the base station is equal for all users. Power controlalleviates the near-far problem at the expense of receiver complexity anddecreased usable bandwidth.

The length is another property of the signature sequences that has tobe taken into consideration. Traditionally signature sequences with a lengthN were used in CDMA so that NTc = T , thus the period of the signaturesequence is equal to the duration of a bit, so each bit is modulated by theentire signature sequence. This kind of signature sequences are so calledshort codes. The disadvantage of using signature sequences with a relativelyshort length is that the crosscorrelations between the signature sequencesvary relatively strongly from each other. Since the crosscorrelations be-tween the signature sequence of a channel and the signature sequence of theother channels determines the amount of interference on the channel, vary-ing crosscorrelations will result in a bit-error-rate performance that variesbetween channels. To solve this so called long codes can be used.

Long codes are signature sequences with a period that is much longerthan the duration of a bit, for example signature sequences with a period of242Tc. When these signature sequences are used to modulate a bit streameach bit will be modulated by a different section of the signature sequence.The amount of interference for a particular bit therefor depends on thecrosscorrelations between the section of the signature sequence that is usedto modulate that bit and the sections of the signature sequences that areused to modulate the bits that are transmitted at the same time in theother channels. This results in an interference on each channel that variesfrom bit to bit, but averaged over the bits there will be the same amount of



interference on each channel. Therefor the bit-error-rate performance on allthe channels will be the same.

2.2 Continuous-time Synchronous CDMA Model

The basic continuous-time synchronous K-user CDMA model describes thereceived signal of a CDMA system in which the bit streams of K synchronoususers antipodally modulate K signature waveforms which are transmittedover an Additive White Gaussian Noise (AWGN) channel. Both the bitstreams and the signature waveforms are represented by Non-Return-to-Zero (NRZ) signals. The received signal for one symbol period in such asystem can be expressed in complex envelope notation as:

r(t) =K∑

k=1

Akbkck(t) + σn(t). (2.1)

Where the following notation is used:

• ck(t) is the real valued deterministic signature waveform assigned tothe kth user, normalized to have unit energy

||ck||2 =∫ T

0c2k(t)dt � 1. (2.2)

The signature waveforms are assumed to be zero outside the interval[0, T ], and therefore, in an AWGN channel, there is no inter symbolinterference.

• Ak is the received amplitude of the kth user’s signal. A2k is referred to

as the energy of the kth user.

• bk ∈ {−1, +1} is a bit transmitted by the kth user.

• n(t) is white Gaussian noise with zero mean and unit variance. It mod-els thermal noise plus other noise sources unrelated to the transmittedsignals. According to (2.1) the noise power in a frequency band withbandwidth B is 2σ2B. In the literature, the one-sided noise spectraldensity 2σ2 is frequently denoted by N0.

2.3 Discrete-time CDMA Model and ConventionalDetection

CDMA detectors commonly have a front-end whose objective is to obtain adiscrete-time representation of the received continuous-time waveform r(t).


2.3. Discrete-time CDMA Model and Conventional Detection

Figure 2.3: Matched filter bank.

One way of converting the received waveform into a discrete-time repre-sentation is to pass it through a matched filter bank, see Figure 2.3, eachmatched to the signature waveform of a different user. The outputs of thematched filters are than sampled at the end of each bit period.

The output of the matched filter for a user k for synchronous CDMAcan be expressed as:

Zmfk=

∫ T

0r(t)ck(t)dt (2.3)

= Akbk

∫ T

0ck(t)ck(t)dt +

∑j �=k

Ajbj

∫ T

0cj(t)ck(t)dt +

σ

∫ T

0n(t)ck(t)dt (2.4)

By using the fact that ck(t) is normalized to have unit energy the matchedfilter outputs can be expressed as

Zmfk= Akbk +

∑j �=k

Ajbjρjk + nk, (2.5)

where

ρjk � 〈cj , ck〉 =∫ T

0cj(t)ck(t)dt (2.6)

and

nk � σ

∫ T

0n(t)ck(t)dt (2.7)

is a Gaussian random variable with zero mean and variance equal to σ2.So the matched filter output consists of a desired signal component, a MAIcomponent and a noise component.



The decisions of the conventional CDMA detector for the bits transmit-ted by user k are based on the sign of the output of the matched filter bankfor user k at the end of each bit period. This detector will perform well whenthe cross correlations ρjk between the signature sequence of the desired userand the signature sequences of the other users in the system are a lot smallerthan the autocorrelation of the signature sequence of the desired user. Theamplitudes A of the signals of all the users in the system have to be aboutequal as well for good performance. The performance of the conventionalCDMA detector will deteriorate however when the number of active usersin the system increases, because then the multiple access interference com-ponent can still become as large as the desired signal component.


Chapter 3

Blind Adaptive MMSEDetection

In this chapter the blind adaptive MMSE detector will be described andmathematically analyzed. This analysis is a summary of the analysis ofblind adaptive MMSE detection in literature ([4], [5] and [6]). First a gen-eral notation for linear multiuser detectors, the class of multiuser detectorsto which the blind adaptive MMSE detector belongs, will be developed. Af-ter that it will be shown that the blind adaptive MMSE detector, whichminimizes the mean output energy, also minimizes the mean square error.Finally, an adaptive algorithm will be derived for the implementation of theblind adaptive MMSE detector. For convenience in this chapter it will beassumed that the desired user is user 1, but the same reasoning can of coursebe applied to all users in the system.

3.1 Linear Multiuser Detectors

The blind adaptive MMSE detector is an example of a linear multiuser detec-tor. Linear multiuser detectors apply a linear transformation to the outputsof the matched filter bank to produce a new set of outputs, which hopefullyprovide better performance when used for estimation. Other examples oflinear multiuser detectors are the conventional, decorrelating and MMSEdetector [4].

Since matched filtering is also a linear operation, the matched filter bankfollowed by a linear transformation used in linear multiuser detection canbe seen as a matched filter bank with modified sequences. So the signaturesequence c is replaced by a modified signature sequence m. A linear mul-tiuser detector for user 1 can be characterized by the modified sequence m1,which is the sum of two orthogonal components. One of these componentsis the signature sequence of user 1, c1. The other component is denoted as


Chapter 3. Blind Adaptive MMSE Detection

x1 and will be referred to as the x sequence, so

m1 = c1 + x1, (3.1)

with m1, c1, x1 ∈ RN , where N is the number of chips per symbol and

〈c1, x1〉 = 0. (3.2)

Since x1 is orthogonal to c1, any x1 can be chosen to minimize the corre-lation between the multiple access interference and m1, while the correlationwith user 1 remains constant. Thus

〈c1, m1〉 = ||c1||2 � 1. (3.3)

The linear detector makes its decision for user 1 based on the sign of theoutput of the matched filter with modified sequence for user 1, so

b1 = sgn(〈r, m1〉). (3.4)

Every linear multiuser detector can be written in this form, so it is a canon-ical representation for linear multiuser detectors [4].

The output of the matched filter with modified sequence for user 1 isequal to

Z1 = 〈r, m1〉= A1b1〈c1, c1 + x1〉 +

K∑k=2

Akbk〈ck, c1 + x1〉 + σ〈n, c1 + x1〉. (3.5)

Using (3.3) and the fact that 〈c1, ck〉 = ρ1k gives

Z1 = A1b1 +K∑

k=2

Akbk(ρ1k + 〈ck, x1〉)

+σ〈n, c1 + x1〉. (3.6)

3.2 Minimizing Mean Output Energy

The blind adaptive MMSE detector in fact minimizes the Mean OutputEnergy (MOE), in contrary to what its name implies. In this section it willbe shown that by minimizing the Mean Output Energy, the Mean SquareError (MSE) is also minimized.

The Mean Output Energy of a linear multiuser detector for user 1 isdefined as:

MOE � E[(〈r, m1〉)2] (3.7)


3.2. Minimizing Mean Output Energy

The trivial solution to minimizing this equation is setting m1 = 0. However,since m1 is defined as the sum of c1 and x1, this solution is eliminated.It can be expected intuitively that minimizing the output energy of thelinear detector is a sensible approach. This is because the energy at theoutput of the detector can be written as the sum of the energy due to thedesired signal plus the energy due to the interference (background noise andmultiple access interference). Any x1, as long as x1 is orthogonal to c1, canbe chosen to minimize the interference, but it will not influence the energyof the desired signal. The x1 that minimizes the Mean Output Energy alsominimizes the Mean Square Error as the following reasoning shows.

The Mean Output Energy and the Mean Square Error of the lineardetector for user 1 can be written as, respectively,

MOE(x1) = E[(〈r, c1 + x1〉)2] (3.8)

and

MSE(x1) = E[(A1b1 − 〈r, c1 + x1〉)2]= E[(A1b1)2 − 2A1b1〈r, c1 + x1〉 + (〈r, c1 + x1〉)2]. (3.9)

Then the fact is used that the received signal r can be decomposed in adesired signal portion A1b1c1 and a residue term R. The residue consists ofmultiple access interference and white Gaussian noise.

MSE(x1) = E[(A1b1)2] − E[2A1b1〈A1b1c1 + R, c1 + x1〉] +E[(〈r, c1 + x1〉)2]. (3.10)

The last term of equation 3.10 is equal to the mean output energy MOE(x1).Since b1 ∈ {−1, +1}, (A1b1)2 = A1

2 and E[(A1b1)2] = A12, equation 3.10

can be written as

MSE(x1) = A12 − E[2(A1b1)2〈c1, c1 + x1〉] −

E[2A1b1〈R, c1 + x1〉] + MOE(x1). (3.11)

Further it is assumed that bit b1 is independent of the other bits bk, k �= 1and that b1 is independent of the white Gaussian noise. From these twoassumptions, it follows that b1 is uncorrelated with the multiple access in-terference. Finally, by also using the obvious fact that b1 is independent ofm1 the term E[2A1b1〈R, c1 +x1〉] can be written as E[2A1b1]E[〈R, c1 +x1〉],so

MSE(x1) = A12 − E[2(A1b1)2〈c1, c1 + x1〉] −

E[2A1b1]E[〈R, c1 + x1〉] + MOE(x1) (3.12)



Since E[2A1b1] = 0, because b1 is equally likely to be 1 or -1, the termE[2A1b1]E[〈R, c1 + c1〉] can be eliminated, resulting in

MSE(x1) = A12 − 2A1

2〈c1, c1 + x1〉 + MOE(x1)= A1

2 − 2A12‖c1‖2 + MOE(x1)

= MOE(x1) − A12. (3.13)

So the mean square error and the mean output energy differ by only aconstant and the arguments that minimize both functions are the same. Toimplement the MSE function in an algorithm, knowledge of the data bits foruser 1 is needed. For an implementation of the MOE function this knowledgeis not needed, which means that an algorithm based on the MOE functiondoes not require training sequences. It can be shown that the mean outputfunction MOE(x1) is strictly convex over the set of signals orthogonal toc1. Therefor, the output energy has no local minima other than the uniqueglobal minimum. With this property, the stochastic gradient descent methodcan be used to adaptively implement the blind adaptive MMSE detector [5].

3.3 Stochastic Gradient Decent Method

The stochastic gradient descent method is based on the gradient decentmethod. The gradient descent method is used to find the parameter θmin

that minimizes the following function:

Ξ(θ) = E[g(X, θ)]. (3.14)

Where X is a random variable and g(·) is a function. If the function Ξis convex, then for any initial condition θ0, the gradient descent algorithmconverges to the minimum of Ξ. The algorithm follows the direction ofsteepest descent (i.e., the direction opposite to the gradient ∇Ξ):

θi = θi−1 − µ∇Ξ(θi−1), (3.15)

where the subscript i is used to indicate the iteration number of the algo-rithm. If the step size µ is arbitrarily small, then eventually θi will be as closeto θmin as desired. In practice, the step size can be progressively decreasedas the algorithm converges. According to (3.14) the probability distribu-tion of X has to be known in order to compute the gradient. Though thisknowledge may be available, the use of these distributions can be avoidedby using the stochastic gradient descent method.

In the stochastic version of the algorithm the unknown term ∇Ξ(θi−1) =∇E[g(X, θi−1)] is replaced by the unaveraged ∇g(Xi, θi−1). With Xi therealization of the random variable X for iteration i. This results in thefollowing stochastic gradient descent algorithm:

θi = θi−1 − µ∇g(Xi, θi−1). (3.16)

where the subscript i again is used to indicate the iteration number.


3.4. Adaptive Implementation

3.4 Adaptive Implementation

The stochastic gradient decent method can be used to find the x sequencexopt that minimizes the Mean Output Energy. The MOE function, given asMOE(x1) = E

[(〈r, c1 + x1〉)2

], is than the equivalent of the Ξ(θ) function,

the x sequence is the equivalent of θ and the received signal r is the equivalentof X. To minimize the Mean Output Energy the x sequence is adaptedeach bit period using the stochastic gradient descent algorithm (3.16). Thismeans that one iteration of the stochastic gradient descent algorithm isperformed for each bit period. Since subscripts are already used to indicateusers, the iteration number is indicated with an index [i]. So the stochasticgradient descent algorithm for adaptation of the x sequence can be writtenas

x1[i] = x1[i − 1] − µ∇(〈r[i], c1 + x1[i − 1]〉)2. (3.17)

Here r[i] indicates the received signal for the bit period of the ith bit in thebit stream.1 x[i−1] is the value of the x sequence obtained from the previousreceived signal r[i − 1] during the previous iteration of the algorithm. Notethat c1 has to remain the same for all bit periods, which implies the use ofa short code CDMA system.

Equation (3.17) requires the gradient of (〈r[i], c1 +x1[i−1]〉)2 for the ithbit interval with respect to x1. This gradient is

∇x1(〈r[i], c1 + x1[i − 1]〉)2 = 2〈r[i], c1 + x1[i − 1]〉r[i]. (3.18)

Equation (3.18) states that the gradient of the mean output energy is equalto a scaled version of the received signal r[i]. After all, 2〈r[i], c1 +x1[i− 1]〉,is only a constant.

At this stage, the gradient descent algorithm for the x sequence can bemodified so that it satisfies the orthogonality condition 〈c1, x1〉 = 0. This isdone by replacing the received signal r[i], by the component of r[i] which isorthogonal to c1. The orthogonal component rort[i] is written as:

rort[i] = r[i] − 〈r[i], c1〉c1. (3.19)

By using the stochastic gradient decent algorithm for the x sequence (3.17),the expression for the gradient (3.18) and the component of the receivedsignal orthogonal to c1 (3.19) the algorithm for minimizing the mean outputenergy can be found:

x1[i] = x1[i − 1] − 2µ〈r[i], c1 + x1[i − 1]〉rort[i]= x1[i − 1] − 2µ〈r[i], c1 + x1[i − 1]〉(r[i] − 〈r[i], c1〉c1) (3.20)

1r[i] is a vector of N samples of the received signal, sampled at the chip times, for theith bit period. Where N is the number of chips per symbol.



The expression 〈r[i], c1〉 in equation (3.20) is a normal matched filteroperation for user 1, as used in the matched filter bank described in Section2.3. The expression 〈r[i], c1 +x1[i−1]〉 in equation (3.20) is a matched filterfor user 1 with modified sequence (3.5). Since the x1 sequence of this filteris adapted by the stochastic gradient descent rule this filter is referred to asthe adaptive filter. The output of the matched filter for user 1 for the ithbit period is written as:

Zmf1[i] = 〈r[i], c1〉. (3.21)

Analogously, the output of the adaptive filter for user 1 for the ith bit periodis written as:

Z1[i] = 〈r[i], c1 + x1[i − 1]〉 = Zmf [i] + 〈r[i], x1[i − 1]〉. (3.22)

Substituting (3.21) and (3.22) in (3.20), the adaptation rule for the x se-quence can be written as:

x1[i] = x1[i − 1] − 2µZ1[i](r[i] − Zmf1 [i]c1). (3.23)

The output of the adaptive filter Z1[i] is used as the decision statistic of theblind adaptive MMSE detector for user 1:

b1[i] = sgn(Z1[i]) = sgn(Zmf [i] + 〈r[i], x1[i − 1]〉). (3.24)

The output energy of the adaptive filter will be minimal when the x1 se-quence has converged to x1,opt, the x sequence that minimizes the meanoutput energy for user 1. In Section 3.2 it was shown that the mean squareerror is than also minimized. So when the x1 sequence has converged tox1,opt the decision statistic for user 1 of the blind adaptive MMSE detectoris equivalent to the decision statistic for user 1 of the MMSE detector. Fig-ure 3.1 gives a graphical representation of the implementation of the blindadaptive MMSE detector.

The natural choice for initialization of the x sequence is x1[0] = 0.Whether the algorithm is stable depends on the value for the step size µ.Equations to determine the maximum value of µ for which the algorithmis still stable are given in [5]. In previous research [3] however the valuesobtained with these equations turned out to result in an unstable algorithm.In practice the value for the step size µ is usually determined by trial-and-error. A smaller step size will result in a longer adaptation time. On theother hand, a smaller step size will also result in an x1[i] which is closer tox1,opt, where x1,opt is the orthogonal sequence component that results in aglobal minimum of the mean output energy. So the best value for µ is atrade-off between adaptation time and accuracy.


3.4. Adaptive Implementation

Figure 3.1: Blind adaptive MMSE detector.


Chapter 4

PIC Detection

In this chapter the Parallel Interference Cancellation (PIC) detector willbe analyzed. The chapter starts with a short discussion of decision-drivendetectors, the class of detectors to which the PIC detecor belongs. After thatthe PIC detector is introduced. Then the different ways in which ParallelInterference Cancellation can be implemented are discussed. Finally furtherrefinements of the implementations of the PIC detector are given, based onmathematical analysis of these PIC implementations in literature.

4.1 Decision-driven Detectors

The idea behind decision-driven detectors is simple: if a decision has beenmade about an interfering user’s bit, then the interfering signal caused bythis user can be reconstructed and subtracted from the received signal. Thiswill cancel the MAI caused by this user, provided that the decision wascorrect; otherwise it will double the contribution to the interference of thisuser.

The simplest decision driven detector is the Successive Interference Can-cellation (SIC) detector, which consists of a bank of matched filters followedby a sorter, see Figure 4.1. In a lot of implementations the sorter sorts thesignals of the different users in order of decreasing received power. However,this is not necessarily best since it fails to take into account the crosscor-relations among users. A sensible alternative is to order users according tothe signal-to-noise ratios computable using

E

[(∫ T

0r(t)ck(t)dt

)2]

= σ2 + A2k +

∑j �=k

A2jρ

2jk, (4.1)

which can be estimated easily from the matched filter outputs. Interferencecancellation for a user k is achieved by subtracting from the matched filteroutputs of user k an estimate of the MAI generated by users with higher


Chapter 4. PIC Detection

Figure 4.1: SIC detector.

received powers than that of user k. For the synchronous case this resultsin the following decision rule:

bk = sgn

Zmfk

−k−1∑j=1

Ajρjk bj

, (4.2)

where it is assumed that the users are numbered in order of decreasingreceived power, so the user with the highest received power has the lowestnumber.

The SIC detector has a number of disadvantages. First of all, the SIC de-tector may actually double the interference, when it makes a wrong decision.Once such an error is made it is likely that the detector will accumulate moreerrors, because the other decisions are dependent on this decision. Since thedemodulation of the first user will never be done in absence of multipleaccess interference, wrong decisions are more likely in the case of a largenumber of users. So performance may decrease rapidly when the number ofusers increases and the performance of the detector for a particular user isgreatly affected by the order in which the users are cancelled. For the samereason, the SIC detector operates best in an unbalanced power environment.This is not a very likely environment in actual cellular wireless CDMA com-munications systems, because those systems usually employ some form ofpower control. Another problem of the SIC detector is that the signals ofthe different users are demodulated sequentially, which causes the delay indemodulating the signals to grow with the number of users.


4.2. PIC Detector

Figure 4.2: Two stage PIC detector.

4.2 PIC Detector

The PIC detector is a detector that also belongs to the class of decision-driven detectors. It alleviates the problem of the SIC detector that theperformance of successive cancellation for a particular user is greatly affectedby the order in which the users are cancelled.

The PIC detector is based on a technique that employs multiple itera-tions in detecting the data bits and cancelling the interference, therefor itis also referred to as Multistage Interference Cancellation (MIC) detector.In its simplest form the PIC detector consists of two stages. The first stageconsists of a conventional bank of matched filters. The second stage per-forms, for each user, reconstruction and subtraction of an estimate of theinterference from all other users, see Figure 4.2. So the second stage in factperforms successive cancellation for all users. This leads to the followingdecision rule:

bk = sgn

yk −

∑j �=k

Ajρjk bj

. (4.3)

The motivation for such a detector is given by comparing with the SICdetector. In the SIC detector, the demodulation of user k is carried outin the presence of the multiple access interference of all users that have aweaker received power. After all, the SIC detector demodulates the receivedsignals in order of decreasing received power. By using the PIC detector,



the interference caused by all interfering users can be estimated trough thebank of matched filters and is then cancelled out. Another advantage of thePIC detector over the SIC detector is that the PIC detector demodulates thesignals of the individual users in parallel, therefor the delay in demodulatingsignals in the PIC detector does not increase with the number of users.

The PIC detector requires more knowledge of the received signal than theconventional CDMA detector. Since it has to reconstruct the transmittedsignal of all the users, it requires information about: the timing of thedesired user, the timing of the interfering users, the received amplitudes andthe signature waveforms of the desired and interfering users. The timing andsignature waveforms of all the users also have to be known in a base stationthat uses conventional CDMA detection, since it has to detect all the users.So PIC slightly increases the processing requirements for a base station,because it will have to implement some form of amplitude estimation.

4.3 PIC Implementation

There are two implementations for PIC detection[7]. The implementationthat was used to describe Parallel Interference Cancellation detection in theprevious section is the so-called narrowband implementation. In this imple-mentation interference is cancelled from the narrowband outputs (matchedfilter outputs or outputs of previous stages) by using the estimates of thedata symbols and channel gains as well as the known cross-correlations be-tween users. This can be clearly seen from Figure 4.2 and equation (4.3).The decision rule of the two-stage narrowband PIC detector for synchronousCDMA given in the previous section can be easily extended to a decisionrule for a multi-stage detector, called a S-stage narrowband PIC detector.For stage s + 1 the decision rule of the S-stage narrowband PIC detectorcan be expressed as

b(s+1)k = sgn

(Z

(s+1)k

)(4.4)

withZ

(s+1)k = Zmfk

−∑j �=k

Ajρjk b(s)j (4.5)

as the decision statistic for stages s > 1 and

Z(1)k = Zmfk

(4.6)

as the decision statistic for stage s = 1. A schematic representation of anS -stage narrowband PIC detector is given in figure 4.3.

The second implementation for PIC detection requires the estimation,regeneration, and cancellation of the signal of each interferer from the re-ceived signal of each of the desired users, see Figure 4.4. Since the widebandsignals of all the users have to be regenerated this implementation is referred


4.3. PIC Implementation

Figure 4.3: S stage narrowband PIC detector.



Figure 4.4: S stage wideband PIC detector.


4.4. Amplitude Estimation

to as the wideband implementation. The decision rule for stage s + 1 of theS -stage wideband PIC detector can be expressed as

b(s+1)k = sgn

(Z

(s+1)k

)(4.7)

with

Z(s+1)k =

∫ T

0r(s)k (t)ck(t)dt (4.8)

as the decision statistic, where the received signal r(s)k for user k at stage s

is estimated according to

r(s)k (t) = r(t) −

K∑j=1

u(s)j (t) (4.9)

and the signal u(s)j (t) corresponds to the reconstructed signal of user j at

stage s. This signal is reconstructed according to

u(s)j (t) = Aj b

(s)j cj(t). (4.10)

At stage s = 1 there has not been any interference cancellation, therefor

r(1)k (t) = r(t). (4.11)

Both implementations of the PIC detector have the same theoretical bit-error-rate performance [7]. For short-code CDMA systems the narrowbandimplementation requires less computations than the wideband implementa-tion, because it avoids regeneration of the wideband signal. For long-codesystems this advantage disappears because in that case the crosscorrelationshave to be recalculated for each symbol anyway. In both cases the narrow-band implementation requires more memory because the crosscorrelationsρjk between the signature sequences of all the users have to be stored.

4.4 Amplitude Estimation

The equations for the decision rules of the narrowband implementation (4.5)and the wideband implementation (4.10) show that both PIC detector im-plementations require knowledge of the received amplitudes of the signals ofall the users. Since this information is not directly available at the receiver,the received amplitudes have to be estimated. A common way to do this isto use the matched filter outputs or outputs of a previous stage, which areboth referred to as soft decisions, as a joint estimation of the detected bitsand the received signal amplitudes. This avoids the use of separate channelestimation algorithms that increase the overall complexity of the receiver.



In this case the decision statistic of the narrowband PIC detector for stagess > 1 (4.5) can be rewritten as

Z(s+1)k = Zmfk

−∑j �=k

Z(s)j ρjk (4.12)

and the equation for the reconstructed signal of the wideband PIC detectorfor stages s > 1 (4.10) can be rewritten as

u(s)j (t) = Z

(s)j cj(t). (4.13)

Unfortunately the amplitude estimates derived from the outputs of thematched filter bank are, especially in the first stages, not very accurate,because they still contain a lot of interference. Therefor enhanced perfor-mance can be achieved at the cost of increased receiver complexity by usingseparate channel estimation algorithms.

4.5 Partial Cancellation PIC

In Correal et al. [8] it is shown that straightforward implementation ofwideband PIC based on complete subtraction of the interference estimatesresults in a biased decision statistic. The bias has its strongest effect in thefirst stage of interference cancellation, in the subsequent stages its effect di-minishes. However if the bias leads to incorrect cancellation at the first stagethe effects of these errors may be observed at the next stages. In Potman [3]it is shown that the decision statistic of a straightforward implementation ofnarrowband PIC, based on complete subtraction of the interference, is alsobiased.

In Correal et al. [8] a simple method to mitigate the effect of the biasand improve the performance of parallel multistage interference cancellationis proposed. This method is based on multiplying the amplitude estimateswith a partial-cancellation factor 0 ≤ C

(s)K ≤ 1 that varies with the stage of

cancellation s and system load K. This multiplication has to be be performedbefore the amplitude estimates are used to subtract the interference in caseof the narrowband implementation, or before the amplitude estimates areused to reconstruct the signal in case of the wideband implementation. Thiscan be interpreted as modifying equation (4.5) and (4.9) to include a partial-cancellation factor C

(s)K resulting in respectively

Z(s+1)k = yk −

∑j �=k

C(s)K Ajρjk b

(s)j (4.14)

for the decision statistic in case of narrowband PIC and

r(s)k (t) = r(t) − C

(s)K

K∑j=1

u(s)j (t) (4.15)


4.5. Partial Cancellation PIC

for the estimated received signal for user k in case of wideband PIC.


Chapter 5

WCDMA Uplink Model

In this chapter a model of the WCDMA uplink is developed. The chapterstarts with a general description of the WCDMA uplink in Section 5.1. Afterthat, in Section 5.2, a general mathematical model of the WCDMA uplinkfor asynchronous multipath fading channels is given.

5.1 WCDMA Uplink

The WCDMA uplink is quite different from the basic CDMA system de-scribed in Chapter 2. Figure 5.1 shows the spreading and modulation in theWCDMA uplink. Instead of just one information stream a user can trans-mit up to six simultaneous information streams in frames over six so calledDedicated Physical Data Channels (DPDCHs). In addition to the six DPD-CHs each user also has one Dedicated Physical Control Channel (DPCCH)available. The WCDMA uplink frame has a duration of 10 ms and is splitinto 15 slots. Each slot of the DPCCH contains pilot bits, Transport FormatCombination Indicator (TFCI) bits, Transmission Power Control (TPC) bitsand Feedback Information (FBI) bits [9].

The information stream(s) that a user wants to transmit over the DPD-CHs are spread to the WCDMA chip-rate of 3.84 Mcps with an OrthogonalVariable Spreading Factor (OVSF) channelization code (cc

k,1 . . . cck,6 in Fig-

ure 5.1). The use of a variable spreading factor makes it possible to supportdifferent data-rates on the DPDCHs. For the WCDMA uplink DPDCHsspreading factors ranging from 4 to 256 are supported. The DPCCH is al-ways spread with an OVSF channelization code with spreading factor 256(cc

k,c in Figure 5.1).The spread DPCCH and DPDCHs are than I-Q/code multiplexed and

the chips of the resulting signal are scrambled with a long or short complexscrambling code (cs

k[i] in Figure 5.1). So WCDMA can be considered along or a short code CDMA system depending on the type of scramblingcodes that are used. The long scrambling codes are Gold codes with 25


Chapter 5. WCDMA Uplink Model

Figure 5.1: WCDMA uplink spreading and modulation.

degree generator polynomials truncated to the 10ms WCDMA uplink framelength, resulting in 38400 chips with 3.84 Mcps. The short scrambling codeshave been chosen from the extended S(2) code family and have a length of256 chips. The complex scrambling sequence is formed, in the case of shortcodes by combining two real valued codes and in the case of long codes bycombining a single sequence with a delayed version of itself.

The complex-valued chip sequence that is the result of the scramblingprocess is split into its real and imaginary parts. Both parts are filteredwith a root-raised cosine pulse-shaping filter with roll-off factor 0.22 and arethan fed to the I and Q branches of the carrier modulator. A more detaileddescription of the UMTS physical layer can be found in [9] and the UMTSphysical layer specification, of which [10] is the overview document.

5.2 General WCDMA Uplink Model

Based on the above description and using a slightly modified version ofthe notation used in the UMTS physical layer specification [10] the complexsymbol gk[i] corresponding with the ith bits of the spread and I-Q/code mul-tiplexed DPDCHs and DPCCH of user k can be mathematically expressedas:

gk[i] =D∑

d=1,3...

βdbdk,d[i]c

ck,d + j

βcb

ck[i]c

ck,c +

D∑d=2,4...

βdbdk,d[i]c

ck,d

(5.1)

where


5.2. General WCDMA Uplink Model

• D is the number of DPDCHs used by user K,

• βd is the gain factor for the DPDCHs,

• bdk,d[i] is the ith bit on the dth Dedicated Physical Data Channel

(DPDCH) of user k,

• cck,d is the real-valued channelization code for the dth DPDCH of user

k,

• βc is the gain factor for the DPCCH,

• bck[i] is the ith bit on the DPCCH of user k,

• and cck,c is the channelization code for the DPCCH of user k.

The transmitted signal of user k is than equal to:

sk(t) = Akp(t)csk[i]gk[i] (5.2)

where

• Ak is the amplitude for user k,

• p(t) is the transmitter pulse shape,

• and csk[i] is the complex-valued long or short scrambling code for user

k used to scramble complex symbol gk[i].

To generate the pulse shape p(t) a root-raised cosine pulse shaping filterwith impulse response

RC0(t) =sin

(π t

Tc(1 − α)

)+ 4α t

Tccos

(π t

Tc(1 + α)

)π t

Tc

(1 −

(4α t

Tc

)2) , (5.3)

is used, where the roll-off factor α is equal to 0.22 and the chip duration TC

is equal to 1chip−rate .

It is assumed that there are K users active in the cell that the modelcovers and that each of these users experiences a Rayleigh fading multipathchannel. This results in the following received signal r(t) at the base station:

r(t) =K∑

k=1

M∑i=1

Lk∑l=1

hk,l(t)sk(t − iT − τk,l) + σn(t) (5.4)

where

• K is the number of active users in the cell that the base station covers,


Chapter 5. WCDMA Uplink Model

• M is the number of complex symbols in a frame,

• Lk is the number of multipaths for user k,

• hk,l(t) is the time dependent complex fading coefficient for multipathl of user k,

• τk,l is the delay of multipath l of user k,

• σ is the standard deviation of the noise,

• and n(t) is white Gaussian noise with zero mean and unit variance.

The blind adaptive MMSE and PIC multiuser detectors that have beenderived for a general CDMA system in the previous two chapters will bederived again for WCDMA in the next two chapters. The consequences forthese detection techniques of the more realistic channel that is assumed inthe WCDMA model will be indicated in the next two chapters as well.


Chapter 6

Blind Adaptive MMSEDetection for WCDMA

In this chapter blind adaptive MMSE detection for WCDMA is described.First a simplified version of the general WCDMA uplink model of the pre-vious chapter is derived in Section 6.1. This simplified model is used todescribe blind adaptive MMSE detection for synchronous AWGN channelWCDMA in Section 6.2. Finally section 6.3 describes generalization to asyn-chronous WCDMA systems and other channel models.

6.1 Synchronous AWGN Short Code WCDMA Up-link Model

To derive an implementation of blind adaptive MMSE detection for WCDMAit is useful to reduce the WCDMA model of the previous chapter to aWCDMA model for a synchronous WCDMA system transmitting over anAWGN channel, since a similar model was used in the derivation in Chapter3. So it is assumed that there is no multipath and no fading and that allusers are synchronous. In that case the received signal (5.4) reduces to:

r(t) =K∑

k=1

sk(t) + σn(t) (6.1)

When short scrambling codes are used the transmitted signal for user k (5.2)can be written as:

sk(t) = Akp(t)cskgk[i] (6.2)

since for short scrambling codes csk[1] = cs

k[2] = . . . = csk[M ] = cs

k. To furthersimplify the model it is also assumed that all users only use one DPDCHand that βd = βc = 1. The expression for the complex symbol (5.1) thanreduces to:

gk[i] = bdk,1[i]c

ck,1 + jbc

k[i]cck,c (6.3)


Chapter 6. Blind Adaptive MMSE Detection for WCDMA

So the received signal can be written as:

r[i] =K∑

k=1

Akp(t)csk

(bdk[i]c

ck,1 + jbc

k[i]cck,c

)+ σn[i]

=K∑

k=1

Akp(t)cskc

ck,1b

dk[i] + jAkp(t)cs

kcck,cb

ck[i] + σn[i] (6.4)

The product of the channelization code and the spreading code will be re-ferred to as the combined code, denoted by cck,d, where the subscript k isused to indicate the user and the subscript d is used to indicate the DPDCHto which the channelization code corresponds. So cc1,1 refers to the com-bined code of DPDCH 1 of user 1 and cc1,c refers to the combined code ofDPCCH of user 1. For convenience it will be assumed that the desired useris user 1. The received signal can then be written as:

r[i] = A1p(t)cc1,1bd1[i] + jA1p(t)cc1,cb

c1[i] + R, (6.5)

where the residue term R consists of multiple access interference and whiteGaussian noise:

R =K∑

k=2

Akp(t)cck,1bdk[i] + jAkp(t)cck,cb

ck[i] + σn[i] (6.6)

6.2 Blind Adaptive MMSE for Synchronous AWGNWCDMA

Recall that the blind adaptive MMSE detector is fully described by a matchedfilter (3.21), an adaptive filter (3.22) and an update-rule for the adaptivefilter coefficients (3.23). Substituting the received signal of the synchronousWCDMA model (6.5) into the equation for the matched filter output (3.21)and replacing the spreading sequence in that equation by the combined codefor DPDCH 1 of user 1 results in the following expression for the output ofthe matched filter for DPDCH 1 of user 1:

Zmf1,1[i] = 〈A1p(t)cc1,1bd1[i] + jA1p(t)cc1,cb

c1[i] + R, cc1,1〉

= 〈A1p(t)cc1,1bd1[i], cc1,1〉 + 〈jA1p(t)cc1,cb

c1[i], cc1,1〉 +

〈R, cc1,1〉= A1p(t)bd

1[i]〈cc1,1, cc1,1〉 + jA1p(t)bc1[i]〈cc1,c, cc1,1〉 +

〈R, cc1,1〉 (6.7)

Where the inner product with itself of the combined code for DPDCH 1 ofuser 1 is:

〈cc1,1, cc1,1〉 =N∑

n=1

cs1[n]cc

1[n]cs1[n]cc

1[n] (6.8)


6.2. Blind Adaptive MMSE for Synchronous AWGN WCDMA

where the overbar is used to indicate the complex conjugate. This can beexpanded to:

〈cc1,1, cc1,1〉 =N∑

n=1

(�(cs1[n]) + j(cs

1[i]))(�(cs1[n]) − j(cs

1[n]))cc1[n]2

=N∑

n=1

(�(cs1[n])2 + (cs

1[i])2)cc

1[n]2

= 2N (6.9)

with N the length in chips of the combined code. The last step follows fromthe fact that �(cs

1[n]) ∈ {−1, 1}, (cs1[i]) ∈ {−1, 1} and cc

1[n] ∈ {−1, 1}. InSection 2.2 the signature sequences were assumed to be normalized to haveunit energy. Equation 6.9 shows that this is not the case in WCDMA. Whenthe output of the matched filter is used in conventional CDMA detectionthis is not of influence, because the sign of the matched filter output is notchanged. However, when the output of the matched filter is used to estimatethe transmitted signal the scaling caused by the signature sequences has tobe taken into account, as will be shown later in this section.

Substituting the received signal of the synchronous WCDMA model (6.5)into the equation for the adaptive filter output (3.22) and replacing thespreading sequence in that equation by the combined code for DPDCH 1 ofuser 1 results in the following expression for the output of the adaptive filterfor DPDCH 1 of user 1:

Z1,1[i] = 〈A1p(t)cc1,1bd1[i] + jA1p(t)cc1,cb

c1[i] + R, cc1,1 + x1,1〉

= 〈A1p(t)cc1,1bd1[i], cc1,1 + x1,1〉 +

〈jA1p(t)cc1,cbc1[i], cc1,1 + x1,1〉 +

〈R, cc1,1 + x1,1〉= A1p(t)bd

1[i]〈cc1,1, cc1,1 + x1,1〉 +jA1p(t)bc

1[i]〈cc1,c, cc1,1 + x1,1〉 +〈R, cc1,1 + x1,1〉

= A1p(t)bd1[i] (〈cc1,1, cc1,1〉 + 〈cc1,1, x1,1〉) +

jA1p(t)bc1[i] (〈cc1,c, cc1,1〉 + 〈cc1,c, x1,1〉) +

〈R, cc1,1〉 + 〈R, x1,1〉 (6.10)

The inner product 〈cc1,1, cc1,1〉 is again equal to 2N . The inner product〈cc1,1, x1,1〉 is equal to zero because x1,1 is orthogonal to cc1,1 by definition.The blind adaptive MMSE detector makes its decisions for the received bitsbased on the sign of the adaptive filter outputs, as indicated by equation(3.24). Since DPDCH 1 is mapped to the real part of the transmittedcomplex symbol, decisions for the received bits on DPDCH 1 are madebased on the sign of the real part of the Z11 matched filter outputs.


Chapter 6. Blind Adaptive MMSE Detection for WCDMA

The update rule for the filter coefficients of the adaptive filter for DPDCH1 of user 1 is found by replacing x1 by x1,1, Z1 by Z1,1, Zmf1[i] by Zmf1,1[i]and c1 by cc1,1 in equation (3.23):

x1,1[i] = x1,1[i − 1] − 2µZ1,1[i](r[i] − Zmf1,1[i]cc1,1). (6.11)

In the term (r[i]−Zmf1,1[i]cc1,1) in the equation above a reconstructed ver-sion of the transmitted signal of user 1 is removed from the received signal,so the remaining signal consists only of interference and noise. Substitutingthe found expressions for the received signal (6.5) and the matched filteroutput (6.7) into this term results in the following equation:

r[i] − Zmf1,1[i]cc1,1 = A1p(t)cc1,1bd1[i] + jA1p(t)cc1,cb

c1[i] + R −

(A1p(t)bd1[i]〈cc1,1, cc1,1〉 +

jA1p(t)bc1[i]〈cc1,c, cc1,1〉 +

〈R, cc1,1〉)cc1,1

= A1p(t)cc1,1bd1[i] + jA1p(t)cc1,cb

c1[i] + R −

A1p(t)bd1[i]〈cc1,1, cc1,1〉cc1,1 +

jA1p(t)bc1[i]〈cc1,c, cc1,1〉cc1,1 +

〈R, cc1,1〉cc1,1 (6.12)

Since the inner product 〈cc1,1, cc1,1〉 is equal to 2N , the reconstructed versionof the received signal of user 1 is 2N times larger than the actual componentof user 1 in the received signal. Therefor the matched filter outputs have tobe scaled with a factor 1

2N when they are used in the update rule for theadaptive filter coefficients. This results in the following final equation forthe update rule for the filter coefficients of the adaptive filter for DPDCH 1of user 1:

x1,1[i] = x1,1[i − 1] − 2µZ1,1[i](r[i] −Zmf1,1

2N[i]cc1,1) (6.13)

The value of the Z1,1 is also scaled by a factor 2N but this can be easilycompensated for by adjusting the step-size µ.

6.3 Asynchronous WCDMA Systems and OtherChannel Models

Equations (6.7), (6.10) and (6.13) describe a blind adaptive MMSE detec-tor for DPDCH 1 of user 1 in a synchronous WCDMA system. Detectorsfor the other DPDCHs and the DPCCH of user 1 can be described by re-placing the channelization code used in those equations by the appropriatechannelization code for the DPDCH that has to be detected. Detectors forthe DPDCHs and DPCCH of other users can be described by replacing the


6.3. Asynchronous WCDMA Systems and Other Channel Models

scrambling code used in equations (6.7), (6.10) and (6.13) by the scramblingcode of the desired user.

Extension to asynchronous systems is also straightforward, just as theconventional detector the blind adaptive MMSE detector can be synchro-nized with the received signal through the use of pilot symbols. Since theblind adaptive MMSE detector has the same input and output parameters asthe conventional CDMA detector it can be used in a rake receiver structureto take advantage of the multipath diversity that is present in multipathchannels. Although the performance of the blind adaptive MMSE detectorwill be negatively influenced by fading, just as the performance of the con-ventional detector, from a functional point of view no special measures arenecessary to use the blind adaptive MMSE detector on fading channels.


Chapter 7

PIC Detection for WCDMA

In this chapter PIC detection for WCDMA is described. First a simpli-fied version of the general WCDMA uplink model of Chapter 5 is derivedin Section 7.1. This simplified model is used to describe PIC detection forsynchronous AWGN channel WCDMA in Section 7.2. Finally section 7.3 de-scribes generalization to asynchronous WCDMA systems and other channelmodels.

7.1 Synchronous AWGN WCDMA Uplink Model

To derive an implementation of PIC detection for WCDMA it is usefulto reduce the WCDMA model of Chapter 5 to a WCDMA model for asynchronous WCDMA system transmitting over an AWGN channel, sincea similar model was used in the derivation in Chapter 4. In contrary tothe model derived in Section 6.1, the model derived in this section will notbe limited to short code WCDMA systems since PIC detection can also beimplemented for long code CDMA systems.

When it is assumed that there is no multipath and no fading and thatall users are synchronous, the received signal (5.4) reduces to:

r(t) =K∑

k=1

sk(t) + σn(t) (7.1)

The transmitted signal of user k (5.2) in that case is equal to:

sk(t) = Akp(t)csk[i]gk[i] (7.2)

To further simplify the model it is also assumed that all users only use oneDPDCH and that βd = βc = 1. The expression for the complex symbol (5.1)than reduces to:

gk[i] = bdk,1[i]c

ck,1 + jbc

k[i]cck,c (7.3)


Chapter 7. PIC Detection for WCDMA

So the received signal can also be written as:

r[i] =K∑

k=1

Akp(t)csk[i]

(bdk[i]c

ck,1 + jbc

k[i]cck,c

)+ σn[i]

=K∑

k=1

Akp(t)csk[i]c

ck,1b

dk[i] + jAkp(t)cs

k[i]cck,cb

ck[i] + σn[i] (7.4)

When it is assumed that the desired user is user 1, the received signal canbe written as:

r[i] = A1p(t)cs1[i]c

c1,1b

d1[i] + jA1p(t)cs

1[i]cc1,cb

c1[i] + R, (7.5)

where the residue term R consists of multiple access interference and whiteGaussian noise:

R =K∑

k=2

Akp(t)csk[i]c

ck,1b

dk[i] + jAkp(t)cs

k[i]cck,cb

ck[i] + σn[i]. (7.6)

The main difference with the model in Section 6.1 is that in the modelin this section the scrambling sequences depend on the indices of the trans-mitted bits, indicated by the use of an index [i] in cs

k[i]. This models thefact that a different section of the scrambling code is used to scramble eachdata bit in long code WCDMA. In short code WCDMA the dependency ofthe scrambling sequences on the indices of the transmitted bits disappearsand the model can be reduced to the model in Section 6.1.

7.2 PIC for Synchronous AWGN WCDMA

In this section a PIC detector for DPDCH 1 of user 1 that works in short-code as well as in long-code synchronous WCDMA system transmitting overan AWGN channel is described. As was stated in Section 4.3, for long-codeCDMA, the narrowband and wideband implementation of the PIC detec-tor have the same theoretical bit-error-rate performance and computationalcomplexity. Since the wideband implementation requires less memory, thewideband implementation will be used in this section.

The wideband PIC detector using soft decision amplitude estimationand partial cancellation is described by a decision rule (4.7), a decisionstatistic (4.8), an estimate of the received signal (4.15) and a reconstructedtransmitted signal (4.13). To arrive at the decision statistic for DPDCH 1of user 1 the single spreading sequence in equation (4.8) has to be replacedwith the combination of scrambling code and channelization code used inWCDMA:

Z1,1 =∫ T

0r(s)1,1(t)c

s1(t)c

c1,1(t) (7.7)


7.3. Asynchronous WCDMA Systems and Other Channel Models

For an estimate of the received signal of DPDCH 1 of user 1 the reconstructedtransmitted signal of the other users in the system is subtracted from thereceived signal, just as in equation (4.15). In addition the reconstructedsignal of the DPCCH of user 1 has to be subtracted from the received signalas well. This results in the following estimate of the received signal ofDPDCH 1 of user 1:

r(s)1,1(t) = r(t) − C

(s)1

jZ

(s)1,c cs

1(t)cc1,c(t) +

K∑j=2

u(s)j (t)

(7.8)

To obtain an equation for the reconstructed transmitted signal of anotheruser in the system the fact that the transmitted signal of a user consists ofa DPDCH signal and a DPCCH signal has to be taken into account. Alsothe single spreading sequence in equation (4.13) has to be replaced with thecombination of scrambling code and channelization code. This results in thefollowing equation for the reconstructed signal:

u(s)j (t) = Z

(s)j,1 cs

j(t)ccj,1(t) + jZ

(s)j,c cs

j(t)ccj,c(t). (7.9)

7.3 Asynchronous WCDMA Systems and OtherChannel Models

Equations (7.7), (7.8) and (7.9) describe a PIC detector for DPDCH 1 of user1 in a synchronous short- or long-code WCDMA system. Just as in the caseof the blind adaptive MMSE detector these equations can be generalized tothe other DPDCHs and the DPCCH of user 1 by replacing the channelizationcode used in those equations by the appropriate channelization code for theDPDCH that has to be detected. Detectors for the DPDCHs and DPCCHof other users can be described by replacing the scrambling code used inequations (7.7), (7.8) and (7.9) by the scrambling code of the desired user.

Extension to asynchronous systems is also straightforward, just as theconventional detector, the PIC detector can be synchronized with the re-ceived signal through the use of pilot symbols. To take advantage of themultipath diversity that is present in multipath channels, the single matchedfilters for each user in each stage of the PIC detector can be replaced bya Rake structure of matched filters. This will however drastically increasethe processing power required by the detector. Although the performanceof the PIC detector will be negatively influenced by fading, just as the per-formance of the conventional detector, from a functional point of view nospecial measures are necessary to use the PIC detector on fading channels.


Chapter 8

WCDMASim

In this chapter WCDMASim, the simulator that is used to study blind adap-tive MMSE and PIC detection for WCDMA, will be described. The chapterstarts with a general description of WCDMASim. Since the uplink is of mostinterest for studying multiuser detection, the WCDMASim uplink simulatorwill be described in more detail in Section 8.2. Section 8.3 describes theextensions required for simulating blind adaptive MMSE and PIC multiuserdetection and other extensions that were made to WCDMASim.

8.1 WCDMASim

WCDMASim is an accurate simulator of the WCDMA physical layer de-veloped by the Mobile and Portable Radio Research Group (MPRG) of theVirginia Polytechnic Institute and State University (Virginia Tech). WCD-MASim strictly adheres to the WCDMA physical layer standards and sim-ulates the WCDMA uplink and downlink over a multiple access specularmultipath Rayleigh fading channel. It uses a conventional Rake receiverwith equal gain combining. WCDMASim is a Matlab program with some ofthe computationally intensive functions implemented as Matlab mex files,written in C.

8.2 WCDMASim Uplink Simulator

The WCDMASim uplink simulator consists of four main blocks: an initial-ization phase block, a desired signal block, a MAI signals block and a Rakereceiver block, as indicated by Figure 8.1. The initialization phase block isonly executed once, before the actual simulation is started. The other blocksare executed for each iteration of the simulation loop. Since WCDMASim isa frame based simulator, one iteration of the simulation loop processes oneWCDMA frame.


Chapter 8. WCDMASim

Initialization Phase

Set simulation parameters (including scrambling sequence)

Generate Record of Fading Signals

(desired mobile only)

Generate symbols for DPCCH

(Control Channel)

Desired Signal

Generate bits for DPDCH

Apply OVSF Spreading to DPDCH and

DPCCH

Apply Scrambling Sequence

Apply Pulse Shaping Filter

Apply Specular Multipath Channel

MAI Signals

Generate symbols for DPDCH and

DPCCH

Apply OVSF Spreading

Apply Scrambling Sequence

Apply Pulse Shaping Filter

Apply Specular Multipath Channel

(if selected)

+

Thermal Noise

This Portion Iterates on a Frame-by-Frame Basis

RAKE ReceiverRake Finger

Matched Filtering and

Decimation to Chip Rate

DescrambleSignalDespread Signal

Estimate Channel Phase

Offset

Correct for Channel Phase

Offset

Combine RAKE Finger OutputsDetect Data BitsCompute Error

Run Vector

Figure 8.1: WCDMASim uplink simulator structure [1].

8.2.1 Initialization Phase Block

In the initialization phase block first some simulation parameters, as forexample noise variance and doppler frequency, are calculated from the sim-ulation parameters specified by the user of the simulator. Then the chan-nelization codes and the scrambling code for the desired user are generated.The pulse shape is generated in this block as well, by taking the desirednumber of samples from a truncated version of the root raised cosine im-pulse response specified in the UMTS physical layer specification. Then thepilot symbols for the desired user are generated and the bits of these pilotsymbols are inserted in the DPCCH frame of the desired user. Two framesof the DPDCHs for the desired user, containing randomly generated bits,are generated in this block as well. The DPCCH frame and the DPDCHframe(s) are than spread with the appropriate OVSF code, I-Q/code multi-plexed, scrambled and pulse shape filtered to generate the transmitted signalfor two frames of the desired user. After that the transmitted signals forthe current and previous frame of the interfering users are generated. TheDPDCH and DPCCH frames that are used to generate these signals bothcontain random data bits.

The initialization phase block of the WCDMASim uplink simulator isalso used to precalculate the fading coefficients of the specular multipathfading channel model that is used. The multipath profile of the channelcan be specified by the user of the simulator by giving delay/relative power


8.2. WCDMASim Uplink Simulator

pairs. For each multipath a series of fading coefficients is calculated bymultiplying its relative power with a series of complex numbers whose am-plitude has Rayleigh distribution and whose phase is uniformly distributedfrom −π to π. Usually, enough fading coefficients for an entire simulationare precalculated in the initialization phase block. Only in very long sim-ulations additional fading coefficients will have to be calculated when theactual simulation is already started. After the fading coefficients are calcu-lated WCDMASim enters the simulation loop.

8.2.2 Desired Signal Block

In the simulation loop first the desired signal block is executed. In this blockfirst an additional frame for each DPDCH, containing random bits, is gener-ated. These frames are spread with the OVSF code, I-Q/code multiplexedtogether with the DPCCH of the desired user, scrambled and pulse shapefiltered. So now three frames of the transmitted signal of the desired userhave been generated. These three frames are needed to be able to select theappropriate delayed parts of the transmitted signal to create the multipathsignal later on. The apply specular multipath channel sub-block of the de-sired signal block takes these three signal frames and processes them trougha specular multipath fading channel. This means that the sub-block firstconcatenates the three frames together into a super-frame. For each mul-tipath the signal samples that correspond with the delay of that multipathare extracted from the super-frame. These samples are multiplied with thefade coefficients and the resulting values for all the multipaths are addedto generate the multipath signal for the desired user. Since calculating fadecoefficients for every sample of the transmitted signal frame is very com-putationally intensive, the simulator applies the fading coefficients to thetransmitted signal samples in a piecewise constant fashion. In practice thismeans that a new fading coefficient is picked once every 400 chips.

8.2.3 MAI Signal Block

The MAI signal block is executed after the desired signal block. The MAIblock performs the same functions for the interfering users as the desiredsignal block did for the desired user. However, to reduce the simulationtimes, application of the specular multipath fading channel is optional forthe interfering users. The output of the MAI signal block is the (multipath)signal for the interfering users. To generate the received signal the simulatoradds the multipath signal of the desired user, the multipath signal of theinterfering users and a noise signal whose variance is determined from thesignal-to-noise-ratio specified for the simulation.


Chapter 8. WCDMASim

8.2.4 Rake Receiver Block

The rake receiver block takes the received signal as input. Since the rakereceiver in the simulator is a assumed to be a ‘perfect’ rake receiver, it hasexact knowledge of all the multipath delays of the channel. This knowledgeis used to generate a delayed version of the received signal for each multipathdelay. Each delayed version of the received signal is first passed trough thereceive filter, which filters the signal with the root raised cosine pulse shapeand decimates the signal to the chip rate. After that each delayed version ofthe received signal is descrambled and despread. The pilot symbols on thedespread DPCCH of the delayed received signal are then used to estimatethe phase offset of the delayed received signal. These phase offset estimatesare used to correct the bit estimates on the DPDCHs and the DPCCH ofthe delayed received signal for their phase offset. The phase corrected bitestimates on the DPDCHs and DPCCH of all the delayed received signalsare than equal gain combined. Finally hard decisions for the bits on theDPDCHs and the DPCCH are made based on the equal gain combineroutputs.

8.3 Extending WCDMASim

WCDMASim has to be extended in order to be able to simulate blind adap-tive MMSE and PIC multiuser detection. Subsection 8.3.1 describes theimplementation of the blind adaptive MMSE detector in WCDMASim andthe changes to the simulator the implementation of this detector required.Subsection 8.3.2 describes the implementation of the PIC detector and thechanges to WCDMASim that were required to implement this detector. Fi-nally Subsection 8.3.3 describes the additional changes, not related to aparticular detector implementation, that were made to WDMASim.

8.3.1 Implementing Blind Adaptive MMSE Detection

Blind adaptive MMSE detection requires a short code CDMA system, asindicated in Section 3.4. The WCDMA specification fulfils this requirementby allowing short scrambling sequences in the uplink as indicated in Section5.1. Although short codes were originally not implemented in WCDMASim,adding short code generation to WCDMASim is relatively straightforward.The Frequency Division Duplex (FDD) spreading and modulation document[11] of the UMTS physical layer specification describes how both the short-and the long UMTS scrambling sequences can be generated using shift reg-isters. The code to generate short scrambling sequences could therefor bederived relatively easily from the long scrambling sequence generation codethat was already present in WCDMASim. Figure 8.2 shows the shift registerconfiguration to generate the UMTS short scrambling sequences.


8.3. Extending WCDMASim

Figure 8.2: Short scrambling sequence generation


Chapter 8. WCDMASim

The blind adaptive MMSE detector implementation has to be added tothe rake receiver block of WCDMASim. The blind adaptive MMSE detec-tor has the same input and output parameters as the conventional CDMAdetector, therefor its implementation does not require any changes to theinput parameters of the rake receiver block. In the rake receiver block somechanges are required. Since WCDMASim is a frame based simulator its con-ventional detector implementation operates on an entire WCDMA frame atonce. So in this implementation, first a delayed version of an entire WCDMAframe is generated with the delay of the multipath that is currently pro-cessed. This delayed frame is then pulse-shape filtered, descrambled anddespread. After that the phase offset of the received signal is determinedfrom the pilot symbols in the DPDCH that has just been despread. Fi-nally the entire frame of DPDCHs and DPCCH bits are corrected for thisphase offset. The blind adaptive MMSE detector however has to update itsadaptive filter coefficients after each detected bit and uses these updatedcoefficients for the detection of the next bit. Therefor in the blind adaptiveMMSE detector implementation in the Rake receiver block the descramblingand despreading of an entire frame that is used in the conventional detectoris replaced with a loop over all the symbols in a frame. Inside this loopequations (6.7), (6.10) and (6.7) are implemented.

At the time this report is written the blind adaptive MMSE detectorimplementation in WCDMASim is still being debugged.

8.3.2 Implementing PIC Detection

Implementation of the PIC detector does require changes to the input pa-rameters of the Rake receiver block, since the PIC detector, in addition tothe desired user, also has to detect the interfering users to perform the can-cellation. Therefor the PIC detector needs information about the timing ofthe interfering users and it needs to know the scrambling and channelizationcodes of the interfering users. This information has to be passed to the Rakereceiver block. In order to be able to do this, changes to the MAI signalblock are required as well, because in the original WCDMASim implemen-tation the channelization and scrambling codes that were used to generatethe MAI are not stored. To implement the actual PIC detector equationsequations (7.7), (7.8) and (7.9) will have to be implemented in the Rakereceiver block of WCDMASim.

At the time this report is written not all the changes described abovehave already been implemented in WCDMASim.


8.3. Extending WCDMASim

8.3.3 Additional Changes

The code of the original WCDMASim uses a mix of different coding styles,resulting in slightly different variable names used for representing the samedata in different parts of the simulator. This can be quite confusing tosomeone not familiar with the code who has to make changes or additionsto the simulator. Therefor parts of WCDMASim were rewritten to make theused coding style more consistent before any other changes to WCDMASimwere made.

To aid the implementation and debugging of blind adaptive MMSE andPIC multiuser detection, the possibility to plot the signals that are presentin different parts of the simulator has been added to WCDMASim. Thismakes it possible to visualize the DPDCH and DPCCH data streams, thechannelization and scrambling codes, the uplink frames, the transmittedsignal, the rayleigh faded transmitted signal, the MAI signal, the noise andfinally the signal that arrives at the receiver.


Chapter 9

Simulation Results

At the time this report is written the blind adaptive MMSE detector andthe PIC detector are only partially implemented in WCDMASim. Thereforthis chapter only contains some preliminary simulation results.

9.1 Data Stream to Received Signal

Figures 9.1 and 9.2 shows the signals that are present in different parts ofWCDMASim, during simulation of a WCDMA system. The system that isbeing simulated has 5 active users and uses short scrambling sequences. Thedesired user uses a spreading factor of 64 for a single DPDCH and moveswith 50 km/h. The simulated channel is a single path channel with a Signalto Noise Ratio (SNR) of 10dB.

Figure 9.1(a) shows the first 8 bits on the DPDCH and the first twobits on the DPCCH of the desired user. The DPDCH and DPCCH arespread with the DPDCH and the DPCCH channelization codes of Figure9.1(b). The spread DPDCH and the DPCCH are mapped to the inphasechannel, respectively the quadrature channel and then multiplied with thecomplex scrambling code of Figure 9.1(c). This results in a complex uplinkframe of which the first 512 chips are shown in Figure 9.1(d). The uplinkframe is filtered with the pulse shaping filter to generate the transmittedsignal of Figure 9.1(e). The velocity of the desired user is used to calculatethe Rayleigh fading coefficients. The transmitted signal is multiplied withthese Rayleigh fading coefficients to obtain the Rayleigh faded signal ofFigure 9.1(f). Figure 9.2(a) shows the output of the MAI Signal Block ofthe simulator and in Figure 9.2(b) the noise is shown. These two signalsare added to the Rayleigh faded signal to obtain the received signal that isshown in Figure 9.2(c).


Chapter 9. Simulation Results

0 1 2 3 4 5 6 7 8

−1

0

1

bit number

DPDCH 1 data

0 1 2

−1

0

1

bit number

DPCCH data

(a) DPDCH and DPCCH bits

0 64 128 192 256 320 384 448 512

−1

0

1

chip number

Channel code DPDCH 1

0 256 512

−1

0

1

chip number

Channel code DPCCH

(b) Channelization codes

0 256 512

−1

0

1

chip number

Scramble code real

0 256 512

−1

0

1

chip number

Scramble code imag

(c) Scrambling code

0 256 512

−2

−1

0

1

2

chip number

Uplink frame real

0 256 512

−2

−1

0

1

2

chip number

Uplink frame imag

(d) Uplink frame

0 1280 2560−2

−1

0

1

2

sample number

Transmitted signal real

0 1280 2560−2

−1

0

1

2

sample number

Transmitted signal imag

(e) Transmitted signal

0 1280 2560−2

−1

0

1

2

sample number

Rayleigh faded signal real

0 1280 2560−2

−1

0

1

2

sample number

Rayleigh faded signal imag

(f) Rayleigh faded signal

Figure 9.1: From data streams to received signal in the WCDMASim simu-lator.


9.1. Data Stream to Received Signal

0 1280 2560−4

−2

0

2

4

6

sample number

MAI signal real

0 1280 2560−4

−2

0

2

4

6

sample number

MAI signal imag

(a) MAI signal

0 1280 2560−10

−5

0

5

10

sample number

Noise real

0 1280 2560−10

−5

0

5

10

sample number

Noise imag

(b) Noise

0 1280 2560−10

−5

0

5

10

15

sample number

Received signal real

0 1280 2560−10

−5

0

5

10

15

sample number

Received signal imag

(c) Received signal

Figure 9.2: From data streams to received signal in the WCDMASim simu-lator (continued).



0 2 4 6 8 10 1210

−3

10−2

10−1

100

SNR(dB)

Bit

Err

or R

ate

Long scramble codesShort scramble codes

Figure 9.3: Bit-error-rate comparison between a long and a short codeWCDMA system.


9.2. Long and Short Scramble Code Comparison

9.2 Long and Short Scramble Code Comparison

Figure 9.3 shows a comparison between the Bit-Error-Rate (BER) of aWCDMA system using long scramble codes and the BER of a system us-ing short scramble codes for a number of Signal to Noise Ratios (SNRs).The system that is being simulated has 4 active users. The desired useruses a spreading factor of 32 for a single DPDCH and moves with 5 km/h.In the simulation a multipath channel is used. To obtain the BER of thesystem for a specific SNR 140 WCDMA frames are simulated. Since oneWCDMA frame contains 38400 chips and the used spreading factor is 32this corresponds with 168000 simulated data bits.

Figure 9.3 shows that in this particular case there is hardly any BERperformance difference between a long and a short scramble code WCDMAsystem. However, as was stated in Section 2.1, the cross correlation betweenshort sequences and thus the experienced interference and BER depend onthe particular short sequences. So to make a statement about the generalityof this result more research will have to be performed on this particularissue.

9.3 Conventional and Blind Adaptive MMSE De-tector Comparison

Figure 9.4 shows a comparison between the BER of a conventional detectorand a blind adaptive MMSE detector for a number of SNR. The WCDMAsystem that is being simulated has 11 active users and uses short scram-bling sequences. The desired user uses a spreading factor of 32 and a singleDPDCH. The desired user does not move and there is no multipath, so anAWGN channel is used. To obtain the BER of the system for a specificSNR 1500 WCDMA frames are simulated. Since one WCDMA frame con-tains 38400 chips and the used spreading factor is 32 this corresponds with1800000 simulated data bits. This means that the BER values for SNR val-ues of 8dB and larger are not very reliable, because these BER values arebased on the occurrence of only a few error events.

In figure 9.4 it can be seen that the blind adaptive MMSE detectorhas about the same BER performance as the conventional detector for thesame SNR. This result was not expected, since blind adaptive MMSE de-tection performed a lot better than conventional detection in simulationsfor a general CDMA system performed in previous research [2] and the-oretically should also perform a lot better in WCDMA. At the momentthe blind adaptive MMSE detector implementation in WCDMASim has notbeen tested enough to make a statement about the cause of this unexpectedresult. Therefor additional simulations of blind adaptive MMSE detectionusing WCDMASim will have to be performed in future research.



2 4 6 8 10 12 1410

−7

10−6

10−5

10−4

10−3

10−2

10−1

SNR(dB)

Bit

Err

or R

ate

conventional detectorblind adaptive mmse detector

Figure 9.4: Bit-error-rate comparison between conventional and blind adap-tive MMSE detection.


Chapter 10

Conclusions andRecommendations

10.1 Conclusions

In this report two multiuser detection algorithms, blind adaptive MMSE de-tection and PIC detection have been analyzed for suitability for applicationin UMTS communications systems. These detection algorithms were firstdescribed for general CDMA communications systems. After that the dif-ferences between general CDMA and WCDMA, the specific type of CDMAthat is used in the physical layer of UMTS, have been described. Also,compared to previous research [3], a more realistic model of the communi-cations channel has been introduced. This was followed by a descriptionof the application of blind adaptive MMSE and PIC detection algorithmsto WCDMA. After that, the changes to WCDMASim, a WCDMA simula-tor, required for simulating blind adaptive MMSE and PIC detection weredescribed. Finally some preliminary simulation results that were obtainedusing the modified WCDMASim were shown. The challenges and problemsthat were encountered while obtaining these simulation results have beendescribed.

Although not straightforward, application of the blind adaptive MMSEand PIC multiuser detection algorithms to WCDMA was found to be pos-sible within the limitations set by the UMTS specification. Implementationof blind adaptive MMSE and PIC multiuser detection in the WCDMASimsimulator however turned out to be more cumbersome.

Adding the blind adaptive MMSE detector (and the short scramblingcode generation it requires) to WCDMASim was relatively easy. But theblind adaptive MMSE requires configuration of some detector parameters.This turned out to be quite hard because of long simulation times. For ex-ample, simulation of a WCDMA system with 11 users, a spreading factor of


Chapter 10. Conclusions and Recommendations

32, one DPDCH per user and a simple AWGN channel without multipathor fading takes 15 seconds for 10 WCDMA frames on a Pentium 4 2.4 GHz.This results in a simulation time of 1.25 ms per simulated bit. So the simu-lation of 1 million bits takes 20 minutes. These long simulation times madeexperimenting with different detector parameters and general debugging ofdetector implementations difficult.

The current implementation of blind adaptive MMSE detection in WCD-MASim does not yet show the improvements in bit-error-rate performancethat were expected based on simulation results obtained for other CDMAcommunications systems in previous research [2]. It is not yet clear if this iscaused by incorrectly chosen detector parameters, bugs in the implementa-tion of the detector in the simulator, or the fact that the influence of MAIon the performance of conventional WCDMA detection is negligible. Inthe latter case, not only blind adaptive MMSE detection, but no multiuserdetection technique in general will show a performance improvement.

Implementation of the PIC detector requires some changes to the overallarchitecture of the WCDMASim simulator. Although these changes arecertainly possible, they require a redesign of the architecture of WCDMASimand have therefor not yet all been implemented in WCDMASim.

So looking back at the goals that were set in Chapter 1 the conclusionsfrom the research described in this report can be summarized as follows:

1. The application of blind adaptive MMSE and PIC multiuser detectionalgorithms to WCDMA is possible within the limitations set by theUMTS specification.

2. Blind adaptive MMSE detection has been implemented in WCDMASim.The WCDMASim simulator requires changes to its software architec-ture for implementation of PIC detection.

3. The preliminary simulation results of blind adaptive MMSE detectiondo not yet show a BER performance improvement compared to conven-tional WCDMA detection. PIC detection has not yet been simulateddue to the changes to the simulator it requires.

After having obtained more experience with WCDMASim, this simulatorturned out to be not as suitable for the project as was expected when it wasinitially chosen. The code of the simulator was inconsistent because of thedifferent coding styles that were used by the different people that apparentlydeveloped the simulator. Also the code of the simulator could have beenmodularized in a better way. These problems have already partially beensolved by rewriting parts of the code of the simulator to make the codingstyle more consistent. But the lack of modularity still remains, which makesapplying changes or additions to the simulator difficult.


10.2. Recommendations and Future Work

10.2 Recommendations and Future Work

To determine the suitability of blind adaptive MMSE detection for WCDMAreliable simulations of this detection technique will have to be performed.This still requires a number of additional research steps:

1. The derivation of blind adaptive MMSE detection for WCDMA willhave to be re-evaluated to make sure it does not contain any mistakes.

2. The implementation of blind adaptive MMSE detection in the simu-lator has to be checked for consistency with the derivation.

3. In Honig et al [5] equations are given to analytically determine theoptimum detector parameters for the blind adaptive MMSE detector.Although some problems with these equations were found in previousresearch [3] it may be useful to study if they are applicable in case ofWCDMA.

4. Additional simulations will have to be performed to gain knowledgeabout the behavior of blind adaptive MMSE detection in WCDMA.

The BER performance of PIC detection cannot be determined usinganalytical techniques [4]. So in order to determine the performance of PICin WCDMA, simulation results for PIC in WCDMA will have to be foundin literature, or this detection technique will have to be implemented in aWCDMA simulator and simulated. Implementation of PIC detection in asimulator is also useful to obtain practical experience with this particulardetection technique.

However because major changes to the architecture of WCDMASim arerequired to implement PIC detection and WCDMASim was found to havesome other problems, as for example long simulation times and bad modular-ity, developing a WCDMA simulator that is more suited for the requirementsof multiuser detection may be considered at this point.


Bibliography

[1] Mobile and Portable Radio Research Group. WCDMASim. Presenta-tion, 2002.

[2] J. Potman, F.W. Hoeksema, and C.H. Slump. DSP Prototypingof Blind Adaptive MMSE Multiuser Detection for Cellular WirelessCDMA Systems. In Proceedings of the ProRISC workshop, Veldhoven,the Netherlands, 28-29 November 2002.

[3] J. Potman. Development of a Multiuser Detection Testbed. Master’sthesis, University of Twente, May 2002.

[4] S. Verdu. Multiuser detection. Cambridge University Press, 1998.

[5] M. Honig, U. Madhow, and S. Verdu. Blind Adaptive Multiuser Detec-tion. IEEE Transactions on Information Theory, 41(4):944–960, July1995.

[6] H. B. Roelofs. Performance Analysis of Wireless Communication Sys-tems Using Fast Simulation. Master’s thesis, University of Twente,December 2001.

[7] R. M. Buehrer, N. S. Correal-Mendoza, and B. D. Woerner. A Simu-lation Comparision of Multiuser Receivers for Cellular CDMA. IEEETransactions on Vehicular Technology, 49(4):1065–1085, July 2000.

[8] N. S. Correal, R. M. Buehrer, and B. D. Woerner. A DSP-BasedDS-CDMA Multiuser Receiver Employing Partial Parallel InterferenceCancellation. IEEE Journal on Selected Areas in Communications,17(4):613–630, April 1999.

[9] H. Holma and A. Toskala, editors. WCDMA for UMTS. John Wiley& Sons, 2001.

[10] Third Generation Partnership Project. Universal Mobile Telecommuni-cations System (UMTS); Physical layer - general description. TechnicalReport ETSI TS 125 201 V5.2.0, European Telecommunications Stan-dards Institute, September 2002.


BIBLIOGRAPHY

[11] Third Generation Partnership Project. Universal Mobile Telecommuni-cations System (UMTS); Spreading and modulation (FDD). TechnicalReport ETSI TS 125 213 V5.2.0, European Telecommunications Stan-dards Institute, September 2002.


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